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Fibonacci: how many calls does each approach make?
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n fib(n) naive calls memo calls table steps
10 55 177 19 9
20 6765 21891 39 19
30 832040 2692537 59 29
40 102334155 331160281 79 39
naive calls = every call the recursion made (counted, not predicted).
memo calls = the same recursion with a notebook: 2n-1 calls, because each F(k) is computed once.
table steps = additions in the bottom-up loop (n-1).